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On-lattice coalescence and annihilation of immobile reactants in loopless lattices and beyond

E. Abad
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Abstract

We study the behavior of the chemical reactions $A+A\to A+S$ and $A+A\to S+S$ (where the reactive species $A$ and the inert species $S$ are both assumed to be immobile) embedded on Bethe lattices of arbitrary coordination number $z$ and on a two-dimensional (2D) square lattice. For the Bethe lattice case, exact solutions for the coverage in the $A$ species in terms of the initial condition are obtained. In particular, our results hold for the important case of an infinite one-dimensional (1D) lattice ($z=2$). The method is based on an expansion in terms of conditional probabilities which exploits a Markovian property of these systems. Along the same lines, an approximate solution for the case of a 2D square lattice is developed. The effect of dilution in a random initial condition is discussed in detail, both for the lattice coverage and for the spatial distribution of reactants.

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E. Abad. 2005-01-11. On-lattice coalescence and annihilation of immobile reactants in loopless lattices and beyond. https://doi.org/10.1103/physreve.70.031110

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